Sharif Digital Repository

Thermalizing quantum systems are conventionally described by statistical mechanics at equilibrium. In contrast, the interplay of disorder and interactions leads to manybody localization (MBL) which avoids thermalization in a closed quantum system.This phenomenon is the only known generic mechanism in which the “eigenstate thermalization hypothesis” is violated. In this vein, localization can protect quantum order even in finite temperature and create emergent nonergodic phases (e.g., time crystal), having no equilibrium counterpart. Yet in the conventional wisdom, the presence of disorder along with the excellent isolation from thermal bath are both necessary for the appearance of the MBL.In... 

The aim of this thesis is to review the spin systems with cluster-type inter-actions. We restrict our attention to one dimentional and exactly solvable models. By "exactly solvable models",we mean the systems which can be mapped to free fermionic systems by Jordan-Wigner transformation.In 2nd chapter we introduce one of the simplest spin systems with cluster-type intraction, the cluster Ising model, and completely derive its statis-tics[10].In chapter 3, we present a classification of topologic phases which can oc-cur in free fermionic gapped systems. This classification is based on sym-metries. Also we'll see that with the help of topological invariants, one can diagnose different... 

The anisotropic Heisenberg ferrimagnet which is composed of two different kind of spins is studied. We have found the exact (factorized) ground state of a general class of ferrimagnets in the presence of a magnetic field which includes the frustrated, anisotropic and long range interactions for arbitrary dimensional space. The factorized ground state is a product of single particle kets on a bipartite lattice composed of two different spins (σ, ρ) which is characterized by two angles, a bi-angle state. The spin waves analysis around the exact ground state show two branch of excitations which is the origin of two dynamics of the model. The signature of these dynamics is addressed as a peak... 

We are interested in the relation between entanglement and quantum phase transitions. We have presented a formulation on how the entanglement of a very large the system is related to the entanglement of a small part of system. The renormalization of entanglement is an indicator of the critical behavior of the models. The framework of our approach is introduced about the Ising model. In particular, we show that derivative of entanglement developes a minimum close to the critical point. We further clarify that this minimum point approaches to the exact critical point of the system as the system becomes thermodynamic. This phenomenon is governed by an exponent that is closely related to the... 

Strongly correlated materials are kind of materials in which novel electric and magnetic properties will appear as a result of strong correlations among their electrons like “heavy fermion materials”. Kondo lattice model is a model to describe heavy fermion materials. If we are merely interested in the magnetic properties of heavy fermions we can replace the Kondo lattice Model with the simpler model called the Kondo-necklace model which consists of the interactions only among the spins of the itinerant (conduction) and localized electrons (magnetic impurities) and also the interactions between the spins of the itinerant electrons. In this thesis we investigate the properties of the one... 

In this thesis, we consider the Kondo-necklace model to investigate the quantum phase transition between the Kondo-singlet and antiferromagnetic phases. There is no exact solution for this model. We would like to study the quantum critical behaviour of this model on one, two and three dimensional spaces in addition to ladder geometry. In this respect, we looked for a proper method which can give us some information for our model on any spaces mentioned above. Therefore, we implemented the perturbation continuous unitary transformation (PCUT) for the Kondo-necklace model. By using this method, we can not only calculate the ground state energy for 1, 2, 3 dimension and n-leg ladder... 

The fascinating subject of heavy fermion physics in rare-earth and actinide systems has been a challenge for theoretical and experimental investigations for decades. Kondo Necklace model is one of the promising models in the study of strongly-correlated heavy fermion compounds, which is studied in this project.One of the methods to diagonalize a Hamiltonian properly, regardless of system size, is the continuous unitary transformation. In this approach, the Hamiltonian is considered as a function of a flow parameter. The Hamiltonian is transformed to a simpler form (diagonal or band-block diagonal) under a flow equation which is based on applying infinite numbers of infinitesimal unitary... 

Entanglement spectrum is the set of eigenvalues of reduced density matrix for a definite state. It contains more information than the entanglement entropy. This spectrum can show entanglement measure, quantum phase transition and topological order in a system. In recent years, the entanglement spectrum for several models has been studied. The entanglement spectrum shows a correspondence to the energy spectrum within some specific regions, which are related to the edge state of the system; It has been verified for the Heisenberg ladder [1] and fractional quantum Hall effect [3]. Moreover, the topological order can be seen in the entanglement spectrum. There exists an acceptable adaption... 

In this thesis, we have implemented the quantum renormalization group method to study quantum spin systems. We reviewed the recent progress to calculate the quantum information properties of these models. The recent investigations show that concurrence and entanglement are two quantities which can show quantum critical properties of the quantum systems. More specifically, the derivative of entanglement and the second derivative of ground state energy show divergent behavior at the quantum critical point. Moreover, the ground state fidelity for two different parameters close to quantum critical point shows a drop which leads to a divergent behavior in its corresponding susceptibility. We have... 

In this thesis, we study the effect of quantum fluctuations by means of a transverse magnetic field () on the ground state of frustrated antiferromagnetic Ising models on the checkerboard and square lattices with nearest neigbor couplings J1 and next-to-nearest neighbor couplings J2. At zero field, such models have exponentially large degenerate classical ground states at J2 ... J1 for the checkerboard lattice and at J2 = 0:5J1 for the square lattice. Quantum fluctuations can have a major role to lift the degeneracies toward a unique quantum ground states. We consider two types of quantum fluctuations, harmonic ones by using linear spin wave theory (LSWT) with single-spin flip excitations... 

Except of few cases the exact, analytic forms of most applicable many-body Hamiltonian ground-states are unknown. Our knowledge in most cases come through computer-based simulations. In recent years a well-structured method has been developed to derive an analytic form for spin Hamiltonian ground-states. ?is method through whi? an analytical fully-factorized ground-state can be derived for many-spin Hamiltonians is independent of the model structure and has unique procedure for any spin Hamiltonian. ?e fully-factorized ground state whi? has been developed, minimizes the energy of the Hamiltonian by minimizing ea? pair-interaction in the Hamiltonian. However, this approval can not be... 

Thermalization or the approach to thermal equilibrium in isolated many-body quantum systems is a fundamental problem in quantum statistical physics. There are various quantum systems, whose properties can be described on the basis of statistical mechanics, but there are also systems in which the thermal equilibrium is not realized.Those, that are integrable or systems that exhibit many-body localization (MBL) due to strong disorder, represent non-thermalized phase. Recent theoretical studies have revealed that integrability and the existence of a static disorder are not necessary conditions for the violation of thermalization, while there are translationally invariant and non-integrable... 

Detecting phase transitions is one of the challenging problems in condensed matter physics. For systems, which show phase transitions, in which an order parameter smoothly becomes nonzero, identifying critical points needs finite-size scaling of very large systems. There also exist phase transitions in nature, that the order parameter is not precisely specified. Hence the detection of the phase transitions is a difficult task. Machine Learning methods are supposed to be powerful tools for investigating phase transition. In this thesis, we first introduce the structure of machine learning algorithms and describe the corresponding building blocks. We then introduce neural networks algorithms... 

Quantum spin liquid (QSL) is an exotic phase of some frustrated magnetic Mott insulators. In this phase, competing interactions result in strong quantum fluctuations which prevent the formation of long-range order even at absolute zero temperature. However, QSL is not solely defined by the absence of order. In the modern definition, it is characterized by fractionalized excitations and emergent gauge fields. The signature of fractional excitations is evident in the form of a broad continuum in conventional probes. However, the continuum spectrum in QSL candidate materials does not definitively indicate whether the continuum is due to fractional excitations or usual ones. Recent theoretical... 

Strongly correlated electron systems are an interesting topic among condensed matter systems. The electrons in such systems are strongly correlated to each other in a way that the behavior of the systems cannot be described by single particle theories. One of the most famous of these systems are heavy fermionic materials which are called so due to heavy quasi particles mass.
This kind of materials have been investigated via different methods. The most im-portant model that can describe characteristics of these materials is Kondo lattice model. When we are only interested in magnetic properties of them, the model can be reduced to Kondo-necklace model which only involves with spin degrees... 

According to Haldane Conjecture Antiferromagnetic Heisenberg Spin Chain with integer spin has an energy gap, and exponential decay of correlation functions , while half integer spin chains are gapless with algebraic decay of correlation functions. A spin chain with two types of spins and Heisenberg interaction shows a mixture of both types of behavior. A ferrimagnet which is composed of two spins (S, s) has two bands of energy, the lower band is gapless and ferromagnetic property while the upper one is gapful with antiferromagnetic behavior. In the present work we have studied the anisotropic ferrimagnet in the presence of a transverse magnetic field. We have shown that the spin wave theory... 

In this thesis, we investigate some transport and many body properties of the 2DEG at the interface of LaAlO3=SrTiO3. First, following Boltzmann approach,we calculate conductivity and mobility of the system. We find that the mobility varies inversely with the cubic power of the carrier density ( / n3 2D) in good agreement with the experimental results. Taking in to account the variations of the dielectric constant of SrTiO3 with carrier density together with the variable impurity density are remarkably important in order to explain the abrupt decrease of the mobility with increasing the density in this system. We find that although the multiband nature of the system and interband... 

Quantum spin liquids are characterized by the lack of long range magnetic order at zero temperature due to strong quantum fluctuations in frustrated magnets, emergent fractionalized excitations coupled to gauge fields, pattern of long-range entanglements, and topological orders. Since the theoretical predictions dated back to the seventies, a huge amount of both theoretical and experimental efforts put forward to explore these emerging phenomena in real materials. Besides the organic compounds with spin liquid ground states, recent years have witnessed the dawn of new oxide materials such as α - RuCl3 and Na2IrO3 which may host spin liquid at low temperatures. The ground states of the latter... 

The concept of topology has underlined the discovery of new phases of matter since the eighties. Meanwhile the material growth, synthesis, and measurements have enabled us to examine the theoretical predictions. Amongst all, the anomalous thermal Hall and Nernst effects result from the non-trivial topological properties of lowenergy carriers. In this thesis our objection is to study some of these phases in two-dimensional magnetic layers such as honeycomb and Kagome lattices and their heterostructures.First, we consider heterostructures of a pyrochlore lattice along the [111] directions: triangular-kagome (TK), triangular-kagome-triangular (TKT), and kagometriangular-kagome (KTK) lattices....